# given the area between two curves, calculate the value of a variable used in both equations

How would you approach this problem?

Find the positive value of c such that the area of the region bounded by the parabolas $y = 25x^2 - c^2$ and $y = c^2 - 25x^2$ is $\frac{8}{15}$

I'm not asking for a full walk through, but I'm just stumped as to where to start. I was thinking of going through the processes of integrating the two curves(as far as it would take me) then setting that equal to 8/15 in order to find the interval. Once the interval was calculated, I would be able to figure out how far away the two parabolas are from each other to find what the value of 'c' is.

Is this the right thought process? or is there a simpler way of finding out the value of c?

Is $c2$ or $c^2$?Well,I think your proccess is right... – HipsterMathematician Aug 26 '12 at 21:25
For one, notice that both parabola will intersect the $x$-axis at $\pm \frac{c}{5}$ (this would be easier to see if you plotted the curves). So $-\frac{c}{5}$ to $\frac{c}{5}$ would be your interval of integration. Other than that, your approach is perfect, integrate the two curves and subtract to get the bounded area and then use that to solve for $c$.